Least Common Multiple (LCM) of 51 and 174
The least common multiple (LCM) of 51 and 174 is 2958.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 51 and 174?
First, calculate the GCD of 51 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 51 ÷ 174 = 0 remainder 51 |
| 2 | 174 ÷ 51 = 3 remainder 21 |
| 3 | 51 ÷ 21 = 2 remainder 9 |
| 4 | 21 ÷ 9 = 2 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 70 | 4690 |
| 99 and 67 | 6633 |
| 36 and 48 | 144 |
| 143 and 26 | 286 |
| 111 and 138 | 5106 |